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Mirrors > Home > ILE Home > Th. List > 2rene0 | GIF version |
Description: 2 is a nonzero real number (common case). (Contributed by David A. Wheeler, 8-Dec-2018.) |
Ref | Expression |
---|---|
2rene0 | ⊢ (2 ∈ ℝ ∧ 2 ≠ 0) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 2re 8908 | . 2 ⊢ 2 ∈ ℝ | |
2 | 2ne0 8930 | . 2 ⊢ 2 ≠ 0 | |
3 | 1, 2 | pm3.2i 270 | 1 ⊢ (2 ∈ ℝ ∧ 2 ≠ 0) |
Colors of variables: wff set class |
Syntax hints: ∧ wa 103 ∈ wcel 2128 ≠ wne 2327 ℝcr 7733 0cc0 7734 2c2 8889 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 604 ax-in2 605 ax-io 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-13 2130 ax-14 2131 ax-ext 2139 ax-sep 4084 ax-pow 4137 ax-pr 4171 ax-un 4395 ax-setind 4498 ax-cnex 7825 ax-resscn 7826 ax-1cn 7827 ax-1re 7828 ax-icn 7829 ax-addcl 7830 ax-addrcl 7831 ax-mulcl 7832 ax-addcom 7834 ax-addass 7836 ax-i2m1 7839 ax-0lt1 7840 ax-0id 7842 ax-rnegex 7843 ax-pre-ltirr 7846 ax-pre-lttrn 7848 ax-pre-ltadd 7850 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-fal 1341 df-nf 1441 df-sb 1743 df-eu 2009 df-mo 2010 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ne 2328 df-nel 2423 df-ral 2440 df-rex 2441 df-rab 2444 df-v 2714 df-dif 3104 df-un 3106 df-in 3108 df-ss 3115 df-pw 3546 df-sn 3567 df-pr 3568 df-op 3570 df-uni 3775 df-br 3968 df-opab 4028 df-xp 4594 df-iota 5137 df-fv 5180 df-ov 5829 df-pnf 7916 df-mnf 7917 df-ltxr 7919 df-2 8897 |
This theorem is referenced by: (None) |
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